I found there is an air duct opening in my basement. It is a 5" round with a flipper (can open and close) extended from the rectangular air duct. Tested and found it is sucking air from basement in to the air duct. Can some one tell me what is the use of this air duct in-take? What is the proper way to deal with it? Thank you.

Since you said the air is going into this 5" round piece of duct I have to assume you have a forced air heating/cooling system and this 5" duct is connected to the return ducting carrying air back to the furnace/air handler from the basement. If there is a supply register bringing air INTO the basement from the air handler/furnace, then this 5" duct is the return for that supply air. Again I will assume any air filter is at the furnace. If there is no supply register in the basement then you may want to cap that 5" duct. All the basement odors will be going throughout the house. There is a slight possibility they needed more return air due to the temperature rise in the furnace. However a 5" duct is too small for that to be a real possibility.